We present the results of an experimental investigation of the lithium based biaxial crystals’ acoustic and acousto-optic properties: lithium selenogallate (LiGaSe2), lithium indium selenide (LiInSe2) and lithium thioindate (LiInS2). The velocities of longitudinal and shear acoustic waves propagating along the crystal axes are determined for the first time. We have also calculated the values of the six elastic constants cii (i = 1-6). In this paper we present the result of the experimental investigation of the acousto-optic figure of merit. We have measured the acousto-optic figure of merit for the first time in the case of diffraction by the longitudinal acoustic waves. Using the obtained experimental data we have computed the values of nine photoelastic coefficients pij (i,j = 1-3) for each investigated lithium based biaxial crystal.